Question

please answer 1-3

year | catch | effort |

1962 | 51.8 | 50.0567 |

1963 | 44.3 | 44.3 |

1964 | 48 | 44.54 |

1965 | 44.826 | 59.9788 |

1966 | 39.208 | 45.3769 |

1967 | 48.278 | 46.6083 |

1968 | 37.819 | 52.2453 |

1969 | 31.992 | 54.1197 |

1970 | 29.894 | 35.6082 |

1971 | 39.406 | 61.2475 |

1972 | 34.279 | 54.7616 |

1973 | 27.958 | 46.5664 |

1974 | 36.407 | 28.5148 |

1975 | 27.827 | 27.1653 |

1976 | 33.71 | 38.8333 |

1977 | 32.888 | 22.0711 |

1978 | 35.804 | 31.362 |

1979 | 38.95 | 25.6873 |

1980 | 29.157 | 19.38 |

1981 | 23.748 | 21.7888 |

1982 | 28.333 | 20.1047 |

1983 | 31.945 | 27.1808 |

1984 | 18.434 | 17.9237 |

1985 | 22.531 | 18.9703 |

1986 | 25.587 | 22.3778 |

1987 | 29.777 | 16.8984 |

1988 | 27.906 | 20.1961 |

1989 | 25.757 | 16.4284 |

1990 | 24.503 | 15.5728 |

1991 | 16.608 | 17.144 |

1992 | 18.162 | 15.7857 |

1993 | 18.371 | 12.1206 |

1994 | 16.993 | 10.3118 |

**ARE 106**

**Quantitative
Methods**

**Problem Set 3**

The data set “BasqueTuna.dat” on Smartsite provides information on the total catch of white tuna in the Basque region of Spain (in tons) and the effort, or total days of fishing (in thousands) to produce this tuna, each year from 1962-1994.

1. Use the data to estimate a simple regression equation of the following form:

*catch**t* =
*b*0 +*b*1*effort**t* +
*e**t*

Report your findings in either table or equation form. Does this regression satisfy CR3? Please show and explain your test for serial correlation at the 95% significance level. Present your results and explain your conclusion

2. Please specify and estimate a better regression model that you can defend, on the basis of economic theory, to explain the production of tuna as a function of effort. Explain why this functional form is better. Present and interpret your results. What is the elasticity of output with respect to effort in this new model?

3. Is serial correlation a problem with the model in (2)? Please carefully present the results of your test for serial correlation (use the 95% significance level), present your results, and explain your findings.

4. Now re-estimate the model in (2) using the Newey-West method. Report your results and compare them with what you got in (2). What is different, and why?

5. Is there evidence that the marginal product of effort has changed over time? How? Please show your work, explaining how you test for this and what you find.

6. Does the model in (5) exhibit serial correlation? Please test for this at the 95% level

and present your test results. Is the result different than in (3)? Please speculate on why or why not.

2

Answer #1

The simple linear regression model is

In our case

y= Dependent variable=Catch

x= Independent variable=Effort

Therefore the model is

After fitting the regression model we get,

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |

Intercept | 16.8113996 | 2.478641652 | 6.782505 | 1.353E-07 | 11.7561766 | 21.86662 | 11.7561766 | 21.866623 |

X Variable 1 | 0.46712366 | 0.070758985 | 6.601616 | 2.243E-07 | 0.32280976 | 0.611438 | 0.32280976 | 0.6114376 |

From the above information we get,

It can be interpreted as follow:

If the effort increase by one unit,the catch is also increase by 0.4671236 unit.

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